Question

Prove the following trigonometric identities

`cos^2 A + 1/(1 + cos^2 A) = 1`

Answer 1

We know that

`sin^2 A + cos^2 A = 1`

`cosec^2 A - cot^2 A = 1`

So,

`cos^2 A + 1/(1 + cot^2 A) = cos^2 A + 1/(cosec A)`

`= cos^2 A + (1/cosecA)^2`

`= cos^2 A + (sin A)^2`

`= cos^2 A + sin^2 A`

= 1